---
title: "A small particle with mass \\(m\\) and positive charge \\(q\\) is released from rest at the origin in a region containing a uniform gravitational field \\(\\vec{g} = -g\\hat{j}\\) and a uniform magnetic field \\(\\vec{B} = B\\hat{k}\\) pointing out of the page. The particle moves in a cycloidal trajectory in the \\(xy\\)-plane. Which of the following correctly pairs the initial horizontal deflection direction of the particle with the ratio \\(F_B / F_g\\) of the magnetic force magnitude to the gravitational force magnitude at the lowest point of its trajectory?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118620/"
date_modified: "2026-08-04T08:12:07+00:00"
---

# A small particle with mass \(m\) and positive charge \(q\) is released from rest at the origin in a region containing a uniform gravitational field \(\vec{g} = -g\hat{j}\) and a uniform magnetic field \(\vec{B} = B\hat{k}\) pointing out of the page. The particle moves in a cycloidal trajectory in the \(xy\)-plane. Which of the following correctly pairs the initial horizontal deflection direction of the particle with the ratio \(F_B / F_g\) of the magnetic force magnitude to the gravitational force magnitude at the lowest point of its trajectory?

A small particle with mass \(m\) and positive charge \(q\) is released from rest at the origin in a region containing a uniform gravitational field \(\vec{g} = -g\hat{j}\) and a uniform magnetic field \(\vec{B} = B\hat{k}\) pointing out of the page. The particle moves in a cycloidal trajectory in the \(xy\)-plane. Which of the following correctly pairs the initial horizontal deflection direction of the particle with the ratio \(F_B / F_g\) of the magnetic force magnitude to the gravitational force magnitude at the lowest point of its trajectory?

![A Cartesian coordinate system with a horizontal x-axis pointing right and a vertical y-axis pointing up, intersecting at the origin labeled (0,0). A small solid circle representing a particle with charge +q and mass m is positioned at the origin. Downward vertical arrows labeled \vec{g} indicate a uniform gravitational field pointing in the negative y-direction. Arrayed across the xy-plane are circular dots with central dots indicating a uniform magnetic field \vec{B} directed out of the page, labeled \vec{B}. No trajectory lines or solution curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831126-0k6too.jpg)

- **A.** Initially deflects to the right; \(F_B / F_g = 1\)
- **B.** Initially deflects to the left; \(F_B / F_g = 2\)
- **C.** Initially deflects to the left; \(F_B / F_g = 1\)
- **D.** Initially deflects to the right; \(F_B / F_g = 2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118620/*